# Or

e1||e2||

is the logical OR function. It evaluates its arguments in order, giving True immediately if any of them are True, and False if they are all False.

# Details

• Or[e1,e2,] can be input in StandardForm and InputForm as . The character can be entered as ||, or, or \[Or].
• Or has attribute HoldAll, and explicitly controls the evaluation of its arguments. In the are evaluated in order, stopping if any of them are found to be True.
• Or gives symbolic results when necessary, removing initial arguments that are False.

# Examples

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## Basic Examples(4)

Combine assertions with ||:

A symbolic disjunction:

A system of equations:

Enter using or:

## Scope(5)

Or works with any number of arguments:

Or is associative:

Or with explicit True or False arguments will simplify:

Or evaluates its arguments in order, stopping when an argument evaluates to True:

The order of arguments may be important:

Symbolic transformations will not preserve argument ordering:

## Applications(6)

Combine conditions in a Wolfram Language program:

If an argument of Or evaluates to True, any subsequent arguments are not evaluated:

The argument order in Or matters; if the last two arguments are reversed, I0 is evaluated:

Combine assumptions:

Combine equations and inequalities; Or is used both in the input and the output:

Use || to combine conditions:

A cellular automaton based on Or:

Find the area of the union of sets given by algebraic conditions:

This shows the set:

## Properties & Relations(7)

Truth table for binary Or:

Ternary Or:

Zero-argument Or is False:

Or with a single argument will return the evaluated argument regardless of value:

&& has higher precedence than ||:

Use BooleanConvert to expand And with respect to Or:

De Morgan's laws relate And, Or, and Not:

Disjunction of conditions corresponds to the Max of Boole functions:

Wolfram Research (1988), Or, Wolfram Language function, https://reference.wolfram.com/language/ref/Or.html (updated 1996).

#### Text

Wolfram Research (1988), Or, Wolfram Language function, https://reference.wolfram.com/language/ref/Or.html (updated 1996).

#### CMS

Wolfram Language. 1988. "Or." Wolfram Language & System Documentation Center. Wolfram Research. Last Modified 1996. https://reference.wolfram.com/language/ref/Or.html.

#### APA

Wolfram Language. (1988). Or. Wolfram Language & System Documentation Center. Retrieved from https://reference.wolfram.com/language/ref/Or.html

#### BibTeX

@misc{reference.wolfram_2024_or, author="Wolfram Research", title="{Or}", year="1996", howpublished="\url{https://reference.wolfram.com/language/ref/Or.html}", note=[Accessed: 23-July-2024 ]}

#### BibLaTeX

@online{reference.wolfram_2024_or, organization={Wolfram Research}, title={Or}, year={1996}, url={https://reference.wolfram.com/language/ref/Or.html}, note=[Accessed: 23-July-2024 ]}